As is known in the art, real-world blood vessel tracking in 3D is a difficult problem, due to the convoluted path of the vessel, frequent proximity to other vessels or blood-filled objects that produce the same intensity, and the effect of pathology, such as stenosis or thrombosis, that narrows or widens the vessel. More particularly, locating the centerline of a blood vessel, given one point at its origin and another point at its terminus in 3D medical data is difficult due mainly to three factors: (1) Vessels cannot be expected to follow the path of a straight line or any other well-described curve; (2) A vessel frequently twists around, or presses tightly against other vessels or blood-filled objects (of similar intensity), resulting in a loss of boundary definition at those positions (i.e., a weak boundary problem); and (3) Vessel pathology (e.g., stenosis, thrombosis) may significantly constrict or expand the vessel, causing a significant change in shape and/or intensity. In some cases, pieces of the vessel may drop entirely out of the data.